Subgroups — C₃×C₅×#2323 #14275357

Order 1920.

1112 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#388	C₂	1	2	yes	maximal
8	C₃×C₅×#388	C₂	1	2	yes	maximal
9	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic
11	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2323	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₂²⋊Q₈	C₄	1	8	yes	complemented
16	C₃×C₄×C₅×Q₈	—	2	4	no	—
17	C₃×C₅×#117	—	2	4	no	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
32	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
33	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₃×C₅×#95	C₂²	1	2	yes	—
35	C₃×C₅×#95	C₂²	1	2	yes	—
36	C₃×C₅×#95	C₂²	1	2	yes	—
37	C₃×C₅×#95	C₂²	1	2	yes	—
38	C₃×C₅×#95	C₂²	1	2	yes	—
39	C₃×#2323	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
41	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
43	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#389	C₂×C₃	1	2	yes	complemented
46	C₅×#388	C₂×C₃	1	2	yes	—
47	C₅×#388	C₂×C₃	1	2	yes	—
48	C₅×#387	C₂×C₃	1	2	yes	complemented
49	C₅×#380	C₂×C₃	1	1	yes	characteristic
50	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅×Q₈	—	2	2	no	—
53	C₂×C₃×C₅×Q₈	—	2	2	no	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂²×C₃×C₄×C₅	—	2	2	no	—
57	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₃×C₅×C₄⋊C₄	—	2	2	no	—
69	C₃×C₅×C₄⋊C₄	—	2	2	no	—
70	C₃×C₅×C₄⋊C₄	—	2	4	no	—
71	C₃×C₅×C₄⋊C₄	—	2	2	no	—
72	C₃×C₅×C₄⋊C₄	—	2	2	no	—
73	C₃×C₅×C₄⋊C₄	—	4	2	no	—
74	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
75	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
76	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
78	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
79	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
80	C₃×C₄²×C₅	—	2	2	no	—
81	C₃×C₄²×C₅	—	2	4	no	—
82	C₃×C₄²×C₅	—	4	2	no	—
83	C₃×C₄²×C₅	D₄	1	4	yes	—
84	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
85	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
87	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
88	C₃×#389	C₂×C₅	1	2	yes	complemented
89	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#388	C₂×C₅	1	2	yes	—
91	C₃×#388	C₂×C₅	1	2	yes	—
92	C₃×#387	C₂×C₅	1	2	yes	complemented
93	C₃×#380	C₂×C₅	1	1	yes	characteristic
94	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
96	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
97	C₅×C₂²⋊Q₈	C₃×C₄	1	8	yes	complemented
98	C₄×C₅×Q₈	—	2	4	no	—
99	C₅×#117	—	2	4	no	—
100	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
104	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
106	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
108	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
111	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
112	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
113	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
115	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
116	C₅×#95	C₂²×C₃	1	2	yes	—
117	C₅×#95	C₂²×C₃	1	2	yes	—
118	C₅×#95	C₂²×C₃	1	2	yes	—
119	C₅×#95	C₂²×C₃	1	2	yes	—
120	C₅×#95	C₂²×C₃	1	2	yes	—
121	#2323	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
122	C₂³×C₃×C₅	—	2	1	no	—
123	C₂³×C₃×C₅	—	2	1	no	—
124	C₂³×C₃×C₅	—	2	1	no	—
125	C₂³×C₃×C₅	—	2	1	no	—
126	C₂³×C₃×C₅	—	2	1	no	—
127	C₂³×C₃×C₅	—	2	1	no	—
128	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
129	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
130	C₃×C₅×Q₈	—	2	8	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	2	1	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	1	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	1	no	—
140	C₂×C₃×C₄×C₅	—	2	1	no	—
141	C₂×C₃×C₄×C₅	—	2	8	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	1	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	1	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
155	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
156	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
157	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
158	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
160	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
161	C₂×C₃×C₄×C₅	#41	1	2	yes	—
162	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
163	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
164	C₃×C₂²⋊Q₈	C₄×C₅	1	8	yes	complemented
165	C₃×C₄×Q₈	—	2	4	no	—
166	C₃×#117	—	2	4	no	—
167	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
170	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
171	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
173	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
176	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
179	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
180	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
182	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
183	C₃×#95	C₂²×C₅	1	2	yes	—
184	C₃×#95	C₂²×C₅	1	2	yes	—
185	C₃×#95	C₂²×C₅	1	2	yes	—
186	C₃×#95	C₂²×C₅	1	2	yes	—
187	C₃×#95	C₂²×C₅	1	2	yes	—
188	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₅×Q₈	—	2	2	no	—
190	C₂×C₅×Q₈	—	2	2	no	—
191	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	—
192	C₂²×C₄×C₅	—	2	2	no	—
193	C₂²×C₄×C₅	—	2	2	no	—
194	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
195	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
197	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
199	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
200	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
201	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
204	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
205	C₅×C₄⋊C₄	—	2	2	no	—
206	C₅×C₄⋊C₄	—	2	2	no	—
207	C₅×C₄⋊C₄	—	2	4	no	—
208	C₅×C₄⋊C₄	—	2	2	no	—
209	C₅×C₄⋊C₄	—	2	2	no	—
210	C₅×C₄⋊C₄	—	4	2	no	—
211	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
212	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
213	C₅×C₂²⋊C₄	—	2	2	no	—
214	C₅×C₂²⋊C₄	—	2	2	no	—
215	C₅×C₂²⋊C₄	—	4	2	no	—
216	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
217	C₄²×C₅	—	2	2	no	—
218	C₄²×C₅	—	2	4	no	—
219	C₄²×C₅	—	4	2	no	—
220	C₄²×C₅	C₃×D₄	1	4	yes	—
221	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
222	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
223	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic
224	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
225	#389	C₂×C₃×C₅	1	2	yes	complemented
226	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
227	#388	C₂×C₃×C₅	1	2	yes	—
228	#388	C₂×C₃×C₅	1	2	yes	—
229	#387	C₂×C₃×C₅	1	2	yes	complemented
230	#380	C₂×C₃×C₅	1	1	yes	characteristic
231	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
232	C₂²×C₃×C₅	—	2	2	no	—
233	C₂²×C₃×C₅	—	2	2	no	—
234	C₂²×C₃×C₅	—	2	2	no	—
235	C₂²×C₃×C₅	—	4	1	no	—
236	C₂²×C₃×C₅	—	4	1	no	—
237	C₂²×C₃×C₅	—	4	1	no	—
238	C₂²×C₃×C₅	—	4	1	no	—
239	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
240	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
241	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
242	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
243	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
244	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
245	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
246	C₃×C₄×C₅	—	2	2	no	—
247	C₃×C₄×C₅	—	2	4	no	—
248	C₃×C₄×C₅	—	2	4	no	—
249	C₃×C₄×C₅	—	2	2	no	—
250	C₃×C₄×C₅	—	2	2	no	—
251	C₃×C₄×C₅	—	4	1	no	—
252	C₃×C₄×C₅	—	4	1	no	—
253	C₃×C₄×C₅	—	4	2	no	—
254	C₃×C₄×C₅	—	4	2	no	—
255	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
256	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₃×Q₈	—	2	2	no	—
258	C₂×C₃×Q₈	—	2	2	no	—
259	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	—
260	C₂²×C₃×C₄	—	2	2	no	—
261	C₂²×C₃×C₄	—	2	2	no	—
262	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
263	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
264	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
265	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
266	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
267	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
268	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
269	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
270	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
271	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
272	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
273	C₃×C₄⋊C₄	—	2	2	no	—
274	C₃×C₄⋊C₄	—	2	2	no	—
275	C₃×C₄⋊C₄	—	2	4	no	—
276	C₃×C₄⋊C₄	—	2	2	no	—
277	C₃×C₄⋊C₄	—	2	2	no	—
278	C₃×C₄⋊C₄	—	4	2	no	—
279	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
280	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
281	C₃×C₂²⋊C₄	—	2	2	no	—
282	C₃×C₂²⋊C₄	—	2	2	no	—
283	C₃×C₂²⋊C₄	—	4	2	no	—
284	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
285	C₃×C₄²	—	2	2	no	—
286	C₃×C₄²	—	2	4	no	—
287	C₃×C₄²	—	4	2	no	—
288	C₃×C₄²	C₅×D₄	1	4	yes	—
289	C₂³×C₅	—	2	1	no	—
290	C₂³×C₅	—	2	1	no	—
291	C₂³×C₅	—	2	1	no	—
292	C₂³×C₅	—	2	1	no	—
293	C₂³×C₅	—	2	1	no	—
294	C₂³×C₅	—	2	1	no	—
295	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
296	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
297	C₅×Q₈	—	2	8	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	8	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
322	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
323	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
324	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
325	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
326	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
327	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
328	C₂×C₄×C₅	C₃×#41	1	2	yes	—
329	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
330	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
331	C₂²⋊Q₈	C₃×C₄×C₅	1	8	yes	complemented
332	C₄×Q₈	—	2	4	no	—
333	#117	—	2	4	no	—
334	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
338	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
340	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
342	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
343	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
345	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
346	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
347	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
348	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
349	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
350	#95	C₂²×C₃×C₅	1	2	yes	—
351	#95	C₂²×C₃×C₅	1	2	yes	—
352	#95	C₂²×C₃×C₅	1	2	yes	—
353	#95	C₂²×C₃×C₅	1	2	yes	—
354	#95	C₂²×C₃×C₅	1	2	yes	—
355	C₂×C₃×C₅	—	4	2	no	—
356	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
357	C₂×C₃×C₅	#519	1	1	yes	characteristic
358	C₂×C₃×C₅	#520	1	1	yes	characteristic
359	C₂×C₃×C₅	#536	1	1	yes	characteristic
360	C₂×C₃×C₅	#537	1	1	yes	characteristic
361	C₂×C₃×C₅	#541	1	1	yes	characteristic
362	C₂×C₃×C₅	#542	1	1	yes	characteristic
363	C₂³×C₃	—	2	1	no	—
364	C₂³×C₃	—	2	1	no	—
365	C₂³×C₃	—	2	1	no	—
366	C₂³×C₃	—	2	1	no	—
367	C₂³×C₃	—	2	1	no	—
368	C₂³×C₃	—	2	1	no	—
369	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
370	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
371	C₃×Q₈	—	2	8	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	8	no	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	2	no	—
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	—	2	2	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	2	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
396	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
397	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
398	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
399	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
400	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
401	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
402	C₂×C₃×C₄	C₅×#41	1	2	yes	—
403	C₂²×C₅	—	2	2	no	—
404	C₂²×C₅	—	2	2	no	—
405	C₂²×C₅	—	2	2	no	—
406	C₂²×C₅	—	4	1	no	—
407	C₂²×C₅	—	4	1	no	—
408	C₂²×C₅	—	4	1	no	—
409	C₂²×C₅	—	4	1	no	—
410	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
411	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
412	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
413	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
415	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
416	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
417	C₄×C₅	—	2	2	no	—
418	C₄×C₅	—	2	4	no	—
419	C₄×C₅	—	2	4	no	—
420	C₄×C₅	—	2	2	no	—
421	C₄×C₅	—	2	2	no	—
422	C₄×C₅	—	4	1	no	—
423	C₄×C₅	—	4	1	no	—
424	C₄×C₅	—	4	2	no	—
425	C₄×C₅	—	4	2	no	—
426	C₄×C₅	C₃×C₄×D₄	1	4	yes	—
427	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	C₂×C₃×C₄×C₅	1	4	yes	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
434	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
435	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
436	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
437	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
438	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
439	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
440	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
441	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
442	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
443	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	4	2	no	—
450	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
451	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	4	2	no	—
455	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	4	no	—
458	C₄²	—	4	2	no	—
459	C₄²	C₃×C₅×D₄	1	4	yes	—
460	C₃×C₅	#2323	1	1	yes	characteristic, direct product factor, Hall
461	C₂²×C₃	—	2	2	no	—
462	C₂²×C₃	—	2	2	no	—
463	C₂²×C₃	—	2	2	no	—
464	C₂²×C₃	—	4	1	no	—
465	C₂²×C₃	—	4	1	no	—
466	C₂²×C₃	—	4	1	no	—
467	C₂²×C₃	—	4	1	no	—
468	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
469	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
470	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
471	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
472	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
473	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
474	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
475	C₃×C₄	—	2	2	no	—
476	C₃×C₄	—	2	4	no	—
477	C₃×C₄	—	2	4	no	—
478	C₃×C₄	—	2	2	no	—
479	C₃×C₄	—	2	2	no	—
480	C₃×C₄	—	4	1	no	—
481	C₃×C₄	—	4	1	no	—
482	C₃×C₄	—	4	2	no	—
483	C₃×C₄	—	4	2	no	—
484	C₃×C₄	C₄×C₅×D₄	1	4	yes	—
485	C₂×C₅	—	4	2	no	—
486	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
487	C₂×C₅	C₃×#519	1	1	yes	characteristic
488	C₂×C₅	C₃×#520	1	1	yes	characteristic
489	C₂×C₅	C₃×#536	1	1	yes	characteristic
490	C₂×C₅	C₃×#537	1	1	yes	characteristic
491	C₂×C₅	C₃×#541	1	1	yes	characteristic
492	C₂×C₅	C₃×#542	1	1	yes	characteristic
493	C₂³	—	2	1	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
500	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
501	Q₈	—	2	8	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
526	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
527	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
528	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
529	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
530	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
531	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
532	C₂×C₄	C₃×C₅×#41	1	2	yes	—
533	C₂×C₃	—	4	2	no	—
534	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
535	C₂×C₃	C₅×#519	1	1	yes	characteristic
536	C₂×C₃	C₅×#520	1	1	yes	characteristic
537	C₂×C₃	C₅×#536	1	1	yes	characteristic
538	C₂×C₃	C₅×#537	1	1	yes	characteristic
539	C₂×C₃	C₅×#541	1	1	yes	characteristic
540	C₂×C₃	C₅×#542	1	1	yes	characteristic
541	C₅	C₃×#2323	1	1	yes	characteristic, direct product factor, Sylow
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
550	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
551	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
552	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
553	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
554	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
555	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
556	C₄	—	2	2	no	—
557	C₄	—	2	4	no	—
558	C₄	—	2	4	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	2	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	C₃×C₄×C₅×D₄	1	4	yes	—
566	C₃	C₅×#2323	1	1	yes	characteristic, direct product factor, Sylow
567	C₂	—	4	2	no	—
568	C₂	C₂×C₃×C₄×C₅×D₄	1	1	yes	characteristic
569	C₂	C₃×C₅×#519	1	1	yes	characteristic
570	C₂	C₃×C₅×#520	1	1	yes	characteristic
571	C₂	C₃×C₅×#536	1	1	yes	characteristic
572	C₂	C₃×C₅×#537	1	1	yes	characteristic
573	C₂	C₃×C₅×#541	1	1	yes	characteristic
574	C₂	C₃×C₅×#542	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
4. C₃×C₅×#391	C₂	semidirect
5. C₃×C₅×#389	C₂	semidirect
6. C₃×C₅×#389	C₂	semidirect
9. C₃×C₅×#387	C₂	semidirect
11. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
12. C₅×#2323	C₃	direct (N × H)
15. C₃×C₅×C₂²⋊Q₈	C₄	semidirect
39. C₃×#2323	C₅	direct (N × H)
41. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
43. C₅×#391	C₂×C₃	semidirect
44. C₅×#389	C₂×C₃	semidirect
45. C₅×#389	C₂×C₃	semidirect
48. C₅×#387	C₂×C₃	semidirect
50. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
85. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
87. C₃×#391	C₂×C₅	semidirect
88. C₃×#389	C₂×C₅	semidirect
89. C₃×#389	C₂×C₅	semidirect
92. C₃×#387	C₂×C₅	semidirect
94. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
97. C₅×C₂²⋊Q₈	C₃×C₄	semidirect
121. #2323	C₃×C₅	direct (N × H)
164. C₃×C₂²⋊Q₈	C₄×C₅	semidirect
222. C₂×C₄×Q₈	C₂×C₃×C₅	semidirect
224. #391	C₂×C₃×C₅	semidirect
225. #389	C₂×C₃×C₅	semidirect
226. #389	C₂×C₃×C₅	semidirect
229. #387	C₂×C₃×C₅	semidirect
231. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
331. C₂²⋊Q₈	C₃×C₄×C₅	semidirect
460. C₃×C₅	#2323	direct (N × H)
541. C₅	C₃×#2323	direct (N × H)
566. C₃	C₅×#2323	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂×C₃×C₄×C₅×Q₈	2
C₂×C₃×C₅×#117	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2323	3
C₃×#2323	5

Subgroups — C3×C5×#2323 #14275357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2323 #14275357